Proposal of Flux-Weakening Control for SPMSM Based on Final State Control Considering Voltage Limit

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1 SPC-11-8 SPMSM Proposal of Flux-Weakening Control for SPMSM Based on Final State Control Considering Voltage Limit Takayuki Miyajima (Yokohama National University) Hiroshi Fujimoto (The University of Tokyo) Masami Fujitsuna (DENSO CORPORATION) Abstract SPMSMs (Surface Permanent Magnet Synchronous Motors) are employed for many industrial applications. SPMSM drive systems should achieve fast torque response and wide operating range. In this paper, in order to fulfill fast response, flux-weakening control based on final state control (FSC) is proposed. FSC settles state variables in final states with feedforward input during finite time. Previously, FSC considering input limit with linear matrix inequality was proposed. It is adapted to two input and two output system as SPMSM in this paper. Finally, simulations and experiments are performed to show that proposed method can achieve fast flux-weakening control. PWM (SPMSM, voltage limit, PWM hold model, final state control, linear matrix inequality ) 1. (SPMSM) d, q (1) PWM () (FF) (3) (4) FF d, q FF (5) (6) (7) (8) (9) (1) (11) (FB) FF (1) (FSC) (13) (14) (LMI) (15) SPMSM d, q FF PWM. SPMSM dq 1 SPMSM dq SPMSM dq y = x = ] T, u = v d v q ] T (1), (), (3) ] } T ẋ(t)=a c(ω e)x(t)b c {u(t) ω ek e (1) y(t)=c c x(t) () ] R 1 ω Ac(ω L e L e) B c := ω e R 1 L L (3) C c I v d, q : d, q R: L: ω e :, q : d, q K e : T (4) T = K mt (4) K mt = P K e, P : 1/6

2 qaxis Decoupling Control max T T k] Current Reference Generator i dk] i qk] C d z] C q z] T u T u T d k] T q k] SVM θ ek] θ ek] i u k] SPMSM i w k] uw θ e k] INV dq k] k] min K mt daxis 1 1 Fig. 1. Block diagram of conventional method 1 Fig.. Point at the intersection of voltage limit circle with constant torque line PWM V k], ±E(E: ) () PWM (5) (6), (7) ON T k] ẋ(t) = A c x(t) B c u(t), y(t) = C c x(t) (5) xk 1] = A s xk] B s T k], yk] = C s xk] (6) A s := e AcTu, B s := e AcTu/ B c E, C s := C c (7) 1 (6), (7), E E T k] 3 SPMSM PWM (1) PWM 1 ω ek e T u E = ( : PWM (8), (9), (1) T = T d ) xk 1] = A s (ω e )xk] B s (ω e ) T q ] T ( T d, q : d, q ON { T k] ] } T ω e K e T u (8) yk] = C sxk] = C cxk] (9) A s (ω e ) := e A c(ω e )T u, B s (ω e ) := e A c(ω e ) Tu Bc (1) SPMSM (16) (11), (1) FB (13) PI C d, q (s) T u Tustin C d, q z] vd v V q > V max(v max := 3 dc : ) C d, q z] v ref d k]=v d ref k] ω e k]l q k] (11) vq ref k]=v qref k] ω ek](l d k] K e) (1) C d, q (s)= L d, qs R, τ = 1T u (13) τs (T : ) d, q i d, i q (14), (15), (16), (17) i dk] = ω ek e L R ωel (i q max )(i q min ) (14) max if T k] > K mt max i qk] = min elseif T k] < K mt min (15) otherwise T k] K mt max := ω ek e R V a R ω el R ω el (16) min := ω ek e R V a R ω el R ω el (17) V a i dk] > i dk] = (Space Vector Modulation: SVM) θ e (=.5ω e T u ) (17) (18) T T k] k] = T k] Tmax if T k] > Tmax (18) T k] otherwise T k] = T d k] T q k]] T (19) 3 T T max (:= 3 u ): dq ON T a T k]: /6

3 T k] T k] Current i k] Reference Generator C1z] B 1 s (ωe)as(ωe)ˆxk] B 1 s (ωe)i k] ωeketu/vdc] T T ffk] T ffk] T k] ˆxk] Pnz] 3 Tu I Vdc Cz] ek] ik] HPWM (SVM) θek] θek] θek] dq uw Fig. 3. Block diagram of conventional method Current Reference Generator Fig. 4. i k] C 1z] 4 T ffk] T k] H PWM (SVM) T ffk] ˆxk] P nz] T u I C z] ek] θ ek] θ ek] ik] θ ek] dq uw Block diagram of proposed method SPMSM INV S (Tu) S (Tu) SPMSM INV FF C 1z] FB C z] (8) () T ff k]=b 1 (ω e)a(ω e)ˆxk]b 1 (ω e)x dk 1] ] T ω ek et u V () dc FF C 1 z] FF C 1z] ˆxk] := î d k] î qk]] T 1 i k1] (18) FB C z] C z] 1 FB C d z], C qz] FF C 1z] 4, 5 FF () FF FSC FF FB SPMSM LMI LMI (8) SPMSM PWM i k] 5 Fig. 5. FSC Trajectory Generator Eq. () B 1 s (ωe)as(ωe)ˆxk] B1 s (ωe)i k] ω ek et u/] T C 1z] C 1 z] T ffk] Feedforward controller C 1 z] of proposed method k =, 1,, N 1 (1) ω e = const. Y = ΣU (1) Y := xn] A N d x] ΣU EMF () ] Σ := A N1 d B d A N d B d B d (3) T U := T T ] T T 1] T T N 1]] (4) U EMF := ω ek e T ] T u 1 1 (5) (1) FF U (6) J = E T QE, Q > (6) E := e1] T e] T en] T ] T (7) ek] := i xk] = i d i q] T xk] (8) ] T A := A d A d A N d (9) B d A d B d B d B := (3) A N1 d B d A N d B d B d I := (i ) T (i ) T (i ) T T (31) E (3) E = I Ax] B (U U EMF ) (3) Σ ΣΣ =, ΣΣ = I Σ R N (N), Σ R N (33) Ũ U := Σ Σ ]Ũ (33) (33) (1) Y = I ]Ũ q R (N) 1 ] T Ũ = Y q (34) (6) (3), (33), (34) (35) 3/6

4 1 SPMSM Table 1. Parameters of SPMSM Inductance L 1.8 mh] Resistance R.157 mω] Pairs of poles P 4 Back EMF constant K e 74.6 mv/(rad/s)] J = R(q) S(q) T QS(q) (35) ) Z := I Ax] B (Σ Y U EMF (36) R(q) := Z T QZ Z T QS(q) (37) S(q) := BΣ q (38) γ J < γ LMI (39) (14) ] γ R(q) S(q) T > (39) S(q) Q 1 LMI SPMSM (4) T T k] T k] = Td k] Tq k] Tmax (k =, 1, N 1) (4) g(i) R N (i := k 1) 1 i i 1 1 g(i) g(i) (41) kt u T k] T k] = g(i)u(q) (41) g(i) (4) (4) {g(i)u(q)} T (g(i)u(q)) Tmax (4) (4) N LMI (43) ] I g(i)u(q) (43) U(q) T g(i) T T max i = k 1, k =, 1, N 1 (39), (43) γ q SPMSM PWM x] xn] N FF U PWM FF 4. SPMSM 1 T u =.1 ms], =36 V] 1 rpm] 6 V a V a =.95V max dq ON T a, dq ON ( )δ (44), (45) T a = T d T q (44) δ = tan 1 T d T q (45) 6(c), 6(g), 6(k) T max 1 ( ) FB FB FF 1 Q = I N N = 38 FSC q d d d q FB FF 5. 1 rpm] = 8 V] n 36 V] n / θ =.9ω et u 7 d 1 FB FF 1 N = 38 FSC 4/6

5 1 1 (a) (Conventional1) 1 (e) (Conventional) (i) (Proposed) (b) (Conventional1) (f) (Conventional) 4 (j) (Proposed) 6 Fig. 6. FSC FF N () FF d q d q PWM N FB FB d, q FB Amplitude of input ms] Amplitude of input ms] Amplitude of input ms] (c) T a (Conventional1) (g) T a (Conventional) Simulation results (k) T a (Proposed) Angle of Input rad] Angle of Input rad] Angle of Input rad] (d) δ (Conventional1) (h) δ (Conventional). (l) δ (Proposed) FB 1 H. Fujimoto, Y. Hori, and A. Kawamura: Perfect Tracking Control based on Multirate Feedforward Control with Generalized Sampling Periods, IEEE Trans. Ind. Eletron., Vol. 48, No. 3, pp , 1. K. P. Gokhale, A. Kawamura, and R. G. Hoft: Deat beat microprocessor control of PWM inverter for sinusoidal output waveform synthesis, IEEE Trans. Ind. Appl., Vol. 3, No. 3, pp , T. Miyajima, H. Fujimoto, and M. Fujitsuna: Control Method for IPMSM Based on Perfect Tracking Control and PWM Hold Model in Overmodulation Range, IPEC-Sapporo 1, pp , 1. 4 T. Miyajima, H. Fujimoto, and M. Fujitsuna: Control Method for IPMSM Based on PWM Hold Model in Overmodulation Range -Study on Robustness and Comparison with Anti-Windup Control-, IEE of Japan Technical Meeting Record, SPC-1-9, pp , 1 (in Japanese). 5 J.-K. Seok, J.-S. Kim, and S.-K. Sul: Overmodulation Strategy for High-Performance Torque Control, IEEE Trans. Power Electronics, Vol. 13, No. 4, pp , B.-H. Bae and S.-K. Sul: A Novel Dynamic Over- 5/6

6 (a) (Conventional1) 5 1 (e) (Conventional) (i) (Proposed) (b) (Conventional1) (f) (Conventional) (j) (Proposed) Fig modulation Strategy for Fast Torque Control of High- Saliency-Ratio AC Motor, IEEE Trans. Ind. Appl., Vol. 41, No. 4, pp , 5. 7 S. Lerdudomsak, S. Doki, and S. Okuma: Novel Voltage Limiter for Fast Torque Response of IPMSM in Voltage Saturation Region, T.IEEJapan, Vol. 18-D, No. 1, pp , 8 (in Japanese). 8 K. Kondo, K. Matsuoka, Y. Nakazawa, and H. Shimizu: Torque feed-back control for salient pole permanent magnet synchronous motor at weakening flux control range, T.IEEJapan, Vol. 119-D, No. 1, pp , 1999 (in Japanese). 9 T.-S. Kwon, G.-Y. Choi, M.-S. Kwak, and S.-K Sul : Novel Flux-Weakening Control of an IPMSM for Quasi-Six-Step Operation, IEEE Trans. Ind. Appl., Vol. 44, NO. 6, pp , 8. 1 H. Nakai, H. Ohtani, E. Satoh, and Y. Inaguma: Development and Testing of the Torque Control for the Permanent-Magnet Synchronous Motor, IEEE Trans. Ind. Electron., Vol. 5, No. 3, pp. 8 86, 5 11 K. Ohi, K. Tobari, and Y. Iwaji: High Response Feild Weakening Control by Voltage Phase Operation, T.IEEJapan, Vol. 19-D, No. 9, pp , 9 (in Japanese). 1 T. Miyajima, H. Fujimoto, and M. Fujitsuna: Proposal of Torque Feedforward Control with Voltage Amplitude of input ms] Amplitude of input ms] Amplitude of input ms] (c) T a (Conventional1) (g) T a (Conventional) Experimental results (k) T a (Proposed) Phase of input rad] Phase of input rad] Phase of input rad] (d) δ (Conventional1) (h) δ (Conventional).4 (l) δ (Proposed) Phase Operation for SPMSM, IEE of Japan Technical Meeting Record, VT-1-1, pp. 17, 1 (in Japanese). 13 T. Totani and H. Nishimura: Final-State Control Using Compensation Input, Trans. of the SICE, Vol. 3, No. 3, pp. 53 6, M. Hirata, T. Hasegawa, and K. Nonami: Seek Control of Hard Disk Drives Based on Final-State Control Tracking Account of the Frequency Compensates and the Magnitude of Control Input, 3th SICE Symposium on Control Theory, pp. 97 1, 1 (in Japanese). 15 S.Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan: Linear Matrix Inequalities in System and Control Theory, Society for Industrial and Applied Mathematics, K. Sakata and H. Fujimoto: Perfect Tracking Control of Servo Motor Based on Precise Model Considering Current Loop and PWM Hold, T.IEEJapan, Vol. 17-D, No. 6, pp , 7 (in Japanese). 17 J. Kudo, T. Noguchi, M. Kawakami, and K. Sano: Mathematical Model Errors and Their Compensations of IPM Motor Control System, IEE of Japan Technical Meeting Record, IEE Japan, SPC-8-5, pp. 5-31, 8 (in Japanese). 6/6

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Proposal of Torque Feedforward Control with Voltage Phase Operation for SPMSM

VT-- SPMSM Proposal of Torque Feedforward Control with Voltage Phase Operation for SPMSM Takayuki Miyajima (Yokohama National University) Hiroshi Fujimoto (The University of Tokyo) Masami Fujitsuna (DENSO